But asked about the proposal Sunday on "Meet the Press," Cain said he was joking.
"That's not a serious plan, that's a joke," Cain said. "I've also said America needs to get a sense of humor. That was a joke, OK?"
Cain went on to say that he would actually secure the border through a combination of a physical fence, technology and possibly the presence of military troops.
But Gonzalez said the idea was no joking matter.
“Mr. Cain has said that America ‘needs to get a sense of humor,’ but I see nothing funny about killing other human beings. Leave the comic routines to the professional comedians," Gonzalez said.
He went on to urge Republican candidates to "immediately repudiate Mr. Cain’s comments and to show strong disapproval of even so-called jokes about killing human beings.”
Minnesota Rep. and fellow White House contender Michele BachmannMichele Bachmann'Real Housewives' producer 'begging' Conway to join cast Ex-rep admires furs amid PETA inaugural gala Why Republicans took aim at an ethics watchdog MORE, speaking at an event in Arizona, said that while she supported building a fence, she believed that immigration policy was not something that Cain should be joking about.
"This is no laughing matter, the border fence," Bachmann said. "We've seen jokes made by presidential candidates about the fence. It is not a joke. This is a real issue, and this is a serious issue."